A theoretically based critical heat flux prediction for rod bundles at PWR conditions

A theoretically based procedure developed for round tubes has been applied to the prediction of DNB heat fluxes in rod bundles at PWR conditions. State-of-the-art subchannel analysis procedures were used to determine local flows and enthalpies. Very good comparison between DNB predictions and experimental observations are found for rod bundles which both uniform and non-uniform axial heat fluxes.     

A critical heat flux approach for square rod bundles using the 1995 Groeneveld CHF table and bundle data of heat transfer research facility

The critical heat flux (CHF) approach using CHF look-up tables has become a widely accepted CHF prediction technique. In these approaches, the CHF tables are developed based mostly on the data bank for flow in circular tubes. A set of correction factors was proposed by Groeneveld et al. [Groeneveld, D.C., Cheng, S.C., Doan, T., 1986. 1986 AECL-UO Critical Heat Flux lookup table. Heat Transf. Eng. 7(1–2), 46] to extend the application of the CHF table to other flow situations including flow in rod bundles. The proposed correction factors are based on a limited amount of data not specified in the original paper. The CHF approach of Groeneveld and co-workers is extensively used in the thermal hydraulic analysis of nuclear reactors. In 1996, Groeneveld et al. proposed a new CHF table to predict CHF in circular tubes [Groeneveld, D.C., et al., 1996. The 1995 look-up table for Critical Heat Flux. Nucl. Eng. Des. 163(1), 23]. In the present study, a set of correction factors is developed to extend the applicability of the new CHF table to flow in rod bundles of square array. The correction factors are developed by minimizing the statistical parameters of the ratio of the measured and predicted bundle CHF data from the Heat Transfer Research Facility. The proposed correction factors include: the hydraulic diameter factor (K_hy), the bundle factor (K_bf), the heated length factor (K_hl), the grid spacer factor (K_sp), the axial flux distribution factors (K_nu), the cold wall factor (K_cw) and the radial power distribution factor (K_rp). The value of constants in these correction factors is different when the heat balance method (HBM) and direct substitution method (DSM) are adopted to predict the experimental results of HTRF. With the 1995 Groeneveld CHF Table and the proposed correction factors, the average relative error is 0.1 and 0.0% for HBM and DSM, respectively, and the root mean square (RMS) error is 31.7% in DSM and 17.7% in HBM for 9852 square array data points of HTRF.     

Tabular method of calculating the critical heat flux in water-cooled triangular rod assemblies

A new method of calculating the critical heat flux in fuel-rod assemblies is presented. The method is based on a generalization of the experimental data in tabular form. The table for the critical heat fluxes is constructed for the correct macrocells of triangular bundles with relative rod spacing s/d=1/4 and a 9.36 mm heat diameter of a microcell for the following conditions: no effect due to peripheral zones and unheated rods; turbulizing influence of the entrance conditions and spacers; and, the heating along the length and across assemblies is uniform. To use the table for other, quite wide regions of the determining parameters, relations are presented for calculating the effect of the important parameters: heating diameter, relative rod spacing in the assembly, distance to the entrance (heated length), turbulizing influence of the spacers, and others. 1 figure, 1 table, 9 references. State Science Center of the Russian Federation—A. I. Leipunskii Physics and Power-Engineering Institute. Translated from Atomnaya énergiya, Vol. 87, No. 1, pp. 17–24, July, 1991.     

Fluid-to-fluid modeling of critical heat flux in 4 × 4 rod bundles

Fluid-to-fluid modeling of critical heat flux (CHF) is to simulate the CHF behaviors for water by employing low cost modeling fluid, and the flow scaling factor is the key to apply the technique to fuel bundles. The CHF experiments in 4×4 rod bundles have been carried out in Freon-12 loop in equivalent nuclear reactor water conditions (P=10.0–16.0 MPa, G=488.0–2100.0 kg/m² s, X_cr=−0.20–0.30). The models in fluid-to-fluid modeling of CHF is verified by the CHF data for Freon-12 obtained in the experiment and the CHF correlation for water obtained by Nuclear Power Institute of China (NPIC) in the same 4×4 rod bundles. It has been found that the S.Y. Ahmad Compensation Distortion model, the Lu Zhongqi model, the Groeneveld model and Stevens–Kirby model overpredict the bundles CHF values for water. Then an empirical correlation of flow scaling factor is proposed. Comparison of the CHF data in two kinds of test sections for Freon-12, in which the distance of the last grid away the end of heated length is different, shows that the spacer grid, which is located at 20 mm away from the end of the heated length, has evidently influenced on the CHF value in the 4×4 rod bundles for Freon-12. This is different from that for water, and the need for further work is required.     

Diameter effect on critical heat flux

The critical heat flux look-up table (CHF LUT) is widely used to predict CHF for various applications, including design and safety analysis of nuclear reactors. Using the CHF LUT for round tubes having inside diameters different from the reference 8 mm involves conversion of CHF to 8 mm. Different authors [Becker, K.M., 1965. An Analytical and Experimental Study of Burnout Conditions in Vertical Round Ducts, Aktiebolaget Atomenergie Report AE 177, Sweden; Boltenko, E.A., et al., 1989. Effect of tube diameter on CHF at various two phase flow regimes, Report IPE-1989; Biasi, L., Clerici, G.C., Garriba, S., Sala, R., Tozzi, A., 1967. Studies on Burnout, Part 3, Energia Nucleare, vol. 14, pp. 530-536; Groeneveld, D.C., Cheng, S.C., Doan, T., 1986. AECL-UO critical heat flux look-up table. Heat Transfer Eng., 7, 46-62; Groeneveld et al., 1996; Hall, D.D., Mudawar, I., 2000. Critical heat flux for water flow in tubes - II subcooled CHF correlations. Int. J. Heat Mass Transfer, 43, 2605-2640; Wong, W.C., 1996. Effect of tube diameter on critical heat flux, MaSC dissertation, Ottawa Carleton Institute for Mechanical and Aeronautical Engineering, University of Ottawa] have proposed several types of correlations or factors to describe the diameter effect on CHF. The present work describes the derivation of new diameter correction factor and compares it with several existing prediction methods.     

Assessment of a DNB-type theoretical critical heat flux model for rod bundles with non-uniform axial power shapes

A general critical heat flux (CHF) prediction method with a wide applicable range and reasonable accuracy is essential to the thermal-hydraulic design and safety analysis at the conceptual design stage for a new pressurized water reactor (PWR). In this study, the Korea Advanced Institute of Science and Technology (KAIST) liquid sub-layer dryout CHF prediction model for Departure from Nucleate Boiling (DNB) region has been implemented in a sub-channel analysis code, and investigated for the method's possible use in a rod bundle environment with various non-uniform axial power shapes. The KAIST model showed comparable prediction capability to Lin's method for bottom-, center-, and top-peaked heat flux shapes. The KAIST model, without any correction factors or empirical constants, turned out to be suitable to fulfill the needs for a basis of a general CHF prediction method as compared to Lin's method and Westinghouse-3 (W-3) correlation.     

Prediction of critical heat flux using ANFIS

The prediction of Critical Heat Flux (CHF) is essential for water cooled nuclear reactors since it is an important parameter for the economic efficiency and safety of nuclear power plants. Therefore, in this study using Adaptive Neuro-Fuzzy Inference System (ANFIS), a new flexible tool is developed to predict CHF. The process of training and testing in this model is done by using a set of available published field data. The CHF values predicted by the ANFIS model are acceptable compared with the other prediction methods. We improve the ANN model that is proposed by Vaziri et al. (2007) to avoid overfitting. The obtained new ANN test errors are compared with ANFIS model test errors, subsequently. It is found that the ANFIS model with root mean square (RMS) test errors of 4.79%, 5.04% and 11.39%, in fixed inlet conditions and local conditions and fixed outlet conditions, respectively, has superior performance in predicting the CHF than the test error obtained from MLP Neural Network in fixed inlet and outlet conditions, however, ANFIS also has acceptable result to predict CHF in fixed local conditions.     

Critical heat flux prediction in vertical bottom-closed rod bundles

This paper presents the analysis of experimental data and calculational relationships for heat the transfer crisis in LWR rod bundle with closed bottom. A new relationship for critical heat flux prediction in the rod bundle with closed bottom based on the improved drift model is described. The comparison of critical heat flux values given by different correlations (including Groeneveld's algorithm used in RELAP5/MOD3.1 Code) and those obtained from the tests in the wide range of regime and geometric parameters is presented.     

A study of the effect of rod-bowing on critical heat flux

An experimental study was carried out to determine the effect of rod-bowing on critical heat flux, using an electrically-heated rod cluster. In this experiment, rod-bow was set to occur in the severest subchannel and axially at the middle between the last two spacers, with uniform axial heat flux. The minimum gap between the outer and inner rods was reduced variously to 1.6 mm, 1.0 mm and zero from the nominal value of 2.1 mm. Other experimental conditions were as follows: pressure 7 MPa; mass velocity 640–2600 kg/m² sec; inlet subcooling 40–560 kJ/kg.Experimental results show only a slight rod-bowing effect, if any, compared with normal spacing, as confirmed by analysis of three-dimensional heat conduction around the rod-bowing area and by the local steam quality deviations calculated by subchannel analyses.     

Critical heat flux prediction in rod bundles under upward low mass flux densities

The analysis of experimental data and results of calculations for heat transfer crisis in heated channels under low upward coolant mass flux densities is presented. This analysis allows the determination of the basic features of the boiling crisis phenomenon. It is shown that the methods currently used for critical heat flux (CHF) prediction have insufficient accuracy in the given range of parameters. A new relationship for the CHF calculation is presented. It should be used for the water–water energy reactor (WWER) and uran–graphite channel reactor—Chernobyl-type (RBMK) rod bundles, and is verified by the test data. The comparison of results obtained by a new CHF correlation and the relationship used in RELAP5/MOD3.1 Code is presented. It is shown that the latter overpredicts the CHF values at atmospheric pressure and for x_cr>0.4 and does not provide conservative estimations for the RBMK fuel bundles.     

On the definition of critical heat flux margin

This paper reviews the current definition of critical heat flux (CHF) margins and discusses their differences.     

A comparative study of correlations of critical heat flux of pool boiling

Nucleate pool boiling is desirable for many engineering systems. One challenge task for designing a system with nucleate pool boiling is to estimate the critical heat flux (CHF), which needs an accurate pool boiling CHF correlation. A few evaluations of pool boiling CHF correlations were reported, which used limited experimental data or covered limited correlations, resulting in inconsistent results. Therefore, it is difficult to determine which one is more appropriate for a given application. In this paper, a database containing 600 data points of pool boiling CHF of 12 pure liquids on plain surfaces having orientation angles of 0°?180° is compiled from 40 published papers. The reduced pressure is from 0.0001 to 0.98, and the 13 fluids are water, helium, nitrogen, hydrogen, R113, FC-72, FC-87, HFE-7100, ethanol, benzene, hexane, pentane, and methanol. With the database, 21 pool boiling CHF correlations are assessed. The most accurate one has a mean absolute deviation of 27.1%, indicating a need for developing more accurate correlations for engineering applications. Besides, the factors affecting the accuracy of correlations are analyzed and some valuable conclusions are obtained. The work lays a valuable foundation for the further study of pool boiling CHF correlations and provides a guide for choosing proper correlations for given applications. Several topics worthy of attention for future studies are suggested.     

Development of critical heat flux correlation for In-vessel retention

ABSTRACT

In-vessel retention (IVR) is a strategy for severe accident management in which the lower head of the reactor vessel is submerged in a water-flooded reactor cavity. Critical heat flux (CHF) data for IVR are important for estimating cooling capacity of the reactor vessel. The existing CHF data for IVR which were obtained for the specific geometries and thermal-hydraulic conditions of actual plants are difficult to be applied to plants with other specifications. Hence, the purpose of this study is to develop CHF correlations applicable to various pressurized water reactor plants in a wide range of thermal outputs based on newly obtained CHF data. A rectangular test section with a cross-section of 150 mm × 150 mm and length of 600 mm was used for simulating a cooling channel. The thermal-hydraulic conditions expected in actual plants were studied, and the results were used in the experiment. The effects of parameters such as pressure, mass flux, thermodynamic quality, and angle on CHF were investigated . Based on these results, we developed a CHF correlation formula that can be applied to a wider range than previously, up to a maximum heat flux of 3000 kW/m², and that predicts CHF with an error of ± 10%.     

Prediction of critical heat flux in vertical pipe flow

A previously developed semi-empirical model for adiabatic two-phase annular flow is extended to predict the critical heat flux (CHF) in a vertical pipe. The model exhibits a sharply declining curve of CHF versus steam quality (X) at low X, and is relatively independent of the heat flux distribution. In this region, vaporization of the liquid film controls. At high X, net deposition upon the liquid film becomes important and CHF versus X flattens considerably. In this zone, CHF is dependent upon the heat flux distribution. Model predictions are compared to test data and an empirical correlation. The agreement is generally good if one employs previously reported mass transfer coefficients.     

Anomalies and other concerns related to the critical heat flux

This paper summarizes various unusual trends in the critical heat flux (CHF) that have been observed experimentally in tubes or bundle subassemblies. They include the following:

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Occurrence of a minimum in the CHF vs. quality (X) curve at high flows - leading to an initial upstream CHF occurrence in uniformly heated channels. This phenomenon has been observed at high flows in both water and Freon.

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Occurrence of a limiting quality region on the CHF vs. X curve where the CHF drops by 30-90% for a nearly constant quality. This is thought to correspond to the boundary between the entrainment controlled and the deposition controlled region and causes problems for prediction methods of the form CHF = f(X).

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Impact of flow obstructions on the occurrence of upstream CHF and the limiting quality region. The additional mixing by grid spacers or bundle appendages results in a more homogeneous phase distribution, and diminishes the effects of flow regime/heat transfer regime transitions responsible for some of the unusual CHF trends, and results in a more gradually decreasing CHF vs. X curve.

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Absence of a CHF temperature excursion at high flows and high qualities - this is found to be caused by a change in slope of the transition boiling part of the boiling curve from a negative value (usual trend that results in a temperature excursion) to a positive slope.

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Gradual disappearance of the sharp temperature excursion at CHF when increasing the pressure towards and beyond the critical pressure - no drastic change is observed in the axial temperature distribution of a heated tube experiencing CHF when, for constant mass flux and inlet temperature, the pressure is gradually increased from subcritical to supercritical.

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CHF fluid-to-fluid modelling: differences in CHF trends at certain conditions between refrigerants and water at equivalent conditions.

The mechanisms responsible for these trends and the implications for bundle geometries are discussed.Concerns regarding the reported uncertainty of predicted CHF values and the range of application of CHF prediction methods are also discussed.     

The critical heat flux for boiling water in tubes

An analysis of the experimental results obtained by various authors on critical heat flux is carried out by using nondimensional criteria. Recommendations are given for the numerical methods of determining values of the critical heat flux in the case of a steam-water mixture, underheated to saturation in tubes and in ring-shaped and plane slotted channels.     

The mechanism and prediction of critical heat flux in inverted geometries

Recent interest in a severe accident management scheme known as ‘In-Yessel Retention’ has created the need to establish the coolability limits of large, inverted geometries. In this paper, full-scale simulations conducted at UCSB's ULPU facility are examined at the microscopic level. Because of the peculiar geometry, it has become possible to directly visualize the boiling transition phenomenon, and with the help of microthermocouples to quantitatively identify the mechanism of dryout. Altogether, a new boiling transition regime was identified, with a significant coupling between overall systems dynamics and the microphenomena. This leads the way to the a priori prediction of critical heat flux and factors that may influence it.     

Calculated effect of radially asymmetric heat generation on temperature and heat flux distribution in a fuel rod

The effect of radially asymmetric heat generation on the temperature and heat flux distribution in a fuel rod is evaluated. Based on practical assumptions, the temperature distribution in power reactor fuel can be obtained between reasonable limits by solving the steady-state heat conduction equation with asymmetric heat generation.